臺灣博碩士論文加值系統

本研究針對磁流體潤滑靜壓軸承之幾何設計、物理參數、偶應力效應及外加磁場效應等的影響，探討磁流體潤滑靜壓軸承的穩態、動態係數與及線性穩定特性。
透過Stoke的微連體理論，加入外部磁場力作用下，將可推導具偶應力效應磁流體潤滑方程式。再以一階微擾法將可進ㄧ步推導磁流體潤滑之Reynolds方程式，並藉由有限差分法分析求解不同的外部磁場力作用潤滑條件下靜壓軸承與毛細管節流器耦合之穩態壓力、靜態及動態特性。此外，也探討節流器參數、軸承運轉參數、磁粒子偶合應力對軸承運轉穩定性的影響。

This thesis studies the characteristics of hydrostatic bearings lubricating with ferrofluid. The multi-pocket capillary compensated bearings has been studied to simulate lubricant film and to determine the influences of magnetic field, magnetic fluid, couple stress parameters, restrictor and geometry and physical parameters of bearing on the static and dynamic performances and stability of a rotor-bearing system.
The modified Reynolds equation is developed by using Stoke couple stress fluid theory as well as Jenkins model. The Reynolds equation is split into the zero-th and first order equations by the method of perturbation. A finite difference method is introduced to solve the zero-th equation for the static pressure and the first order equations for the dynamic pressure distributions of the hydrostatic journal bearing. Static analyses determine the static pressure distribution, load capacity, flow rate and friction coefficient, and dynamic analyses determine the stiffness and damping coefficients. In advance, stability maps of a rotor-bearing system are determined by Routh-Hurwitz method.

摘要………………………………………………………………………… i
ABSTRACT………………………………………………………………… ii
誌謝……………………………………………………………………… iii
目錄………………………………………………………………………… iv
圖目錄……………………………………………………………………… vi
符號表…………………………………………………………………… viii
第一章、緒論……………………………………………………………… 1
1.1前言……………………………………………………………… 1
1.2研究目的………………………………………………………… 2
第二章、文獻回顧………………………………………………………… 3
2.1動壓軸承………………………………………………………… 3
2.2靜壓軸承………………………………………………………… 4
2.3磁流體流變特性………………………………………………… 8
2.4磁流體潤滑分析…………………………………………………11
第三章、理論分析………………………………………………………… 13
3.1軸承潤滑模式……………………………………………………13
3.2節流器流量守恆方程式…………………………………………19
3.3統御方程式線性化………………………………………………20
3.4磁場模型Magnetic models………………………………… 21
3.4.1模型1-同心有限導線磁場模型…………………………21
3.4.2模型2-偏位無限長導線磁場模型………………………22
3.4.3模型3-偏位有限長導線磁場模型………………………22
3.5靜態性能…………………………………………………………22
3.6軸承油膜動態係數………………………………………………23
3.7軸承/轉子穩定性分析………………………………………… 24
第四章、結果與討論……………………………………………………… 25
第五章、結論……………………………………………………………… 36
參考文獻…………………………………………………………………… 37
個人簡介…………………………………………………………………… 44

[1]W. J. Harrison, “The Hydrodynamical Theory of Lubrication of a Cylindrical Bearing Under Variable Load and of a Pivot Bearing,” Transactions of the Cambridge Philosophical Society, Vol. 22, pp. 373 -388, 1919.
[2]O.Pinkus and B. Sternlicht, “Theory of Hydrodynamic Lubrication,” McGraw-Hill, New-York, 1961.
[3]J. W. Lund, “Review of the concept of dynamic coefficients for fluid film journal bearings,” J. of Tribology, Vol. 109, pp. 37-41, 1987.
[4]J. W. Lund and K. K. Thomsen, “Calculation method and data for the dynamic coefficients of oil lubricated journal bearings,” Topics in Fluid Film Bearing and Rotor Bearing System Design and Optimization ASME, pp. 1-28, 1978.
[5]A. Petchenev, D. E. Bently, P. Goldman, “1/3 Whirl Phenomenon: Case History on Vibration Response of a Rotor Supported in One Rigid and One Poorly Lubricated Fluid-Film Bearing,” Bently Rotor Dynamic Research Corporation, Report No. 6, 1999.
[6]A. Petchenev, P. Goldman, A. Muszynska, D. E. Bently, “Analytical Study on the Fluid Journal Bearing/Seal/Rotor System,” FED-Vol.207, The Joint ASME &; JSME Fluids Engineering Annual Conference, Hilton Head Isl., SC, p.33-38, 1995.
[7]P. Goldman, A. Petchenev, D. E. Bently, A. Muszynska, “Torque and Power Loss in a Cylindrical Fluid-Lubricated Earing/Rotor System,” 96-GT-408, IGTI/ASME TURBO EXPO, Birmingham, UK, pp.1-6, 1996.
[8]D. E. Bently, A. Petchenev, “Dynamic stiffness and the advantages of externally pressurized fluid film bearings,” ORBIT, Vol. 21, pp. 18-24, 2000.
[9]S. Heller and W. Shaprio, “A Numerical Solution for the Incompressible Hybrid Journal Bearing With Cavitation,” ASME Journal of Lubrication Technology, Vol. 91, No. 3, pp.508-515, 1969.
[10]J. P. O’Donoghue, W. B. Rowe and C. J. Hooke, “Design of Hydrostatic Using an Operating Parameter,” Wear, Vol. 14, pp. 355-362, 1969.
[11]W. B. Rowe, J. P. O’Donoghue and A. Cameron, “Optimization of Externally Pressurized Bearings for Minimum Power and Low Temperature Rise,” Tribology, Vol. 3, pp.153-157, 1970.
[12]B. Ghosh, “An Exact Analysis of a Hydrostatic Journal Bearing with a Large Circumferential Sill,” Wear, Vol. 21, pp.367-375, 1972.
[13]B. Ghosh, “Load And Flow Characteristics of Capillary-Compensated Hydrostatic Journal Bearing,” Wear Vol. 23, pp.377-386, 1973.
[14]R. Leonard and W. B. Rowe, ”Dynamic Force Coefficients the Mechanism of Instability in the Hydrostatic Journal Bearings,” Wear, Vol. 23, pp.277-282, 1973.
[15]S. M. Rohde and H. A. Ezzat, “On the Dynamic Behavior of Hybrid Journal Bearings,” ASME Journal of Lubrication Technology, Vol. 98, pp.90-94, 1976.
[16]M. K. Ghosh, “Dynamic Characteristics of Multirecess Externally Pressurized Oil Journal Bearing,” ASME Journal of Lubrication Technology, Vol. 100, pp.467-471, 1978.
[17]M. K. Ghosh, B. C. Majumdar and J. S. Rao, “Steady-State and Dynamic Behaviour of Multi-Recess Hybrid Oil Journal Bearings,” Journal of Mechanical Engineering Science, Vol. 21, pp.345-351, 1979.
[18]M. K. Ghosh and N. S. Viswanath, “Recess Volume Fluid Compressibility Effect on the Dynamic Characteristics of Multirecess Hydrostatic Journal Bearings with Journal Rotation,” ASME Journal of Tribology, Vol. 109, pp. 417-426, 1987.
[19]M. K. Ghosh, S. K. Guha and B. C. Majumdar, ”Rotordynamic Coefficients of Multirecess Hybrid Journal Bearings Part I, ” Wear, Vol. 129, pp. 245-259, 1989.
[20]C. H. Chen, Y. Kang, Y. P. Chang, Y. P. Wang, H. H. Lee, “Influences of restrictor on stability of the rigid rotor-hybrid bearings system,” Journal of Sound and Vibration, Vol. 297, No. 2, pp. 635-648, 2006.
[21]C. H. Chen, Y. Kang, Y. P. Chang, H. H. Lee, P. C. Shen, “Influences of recess depth on the stability of the Jeffcott rotor supported by hybrid bearings with orifice restrictors,” Industrial Lubrication and Tribology, Vol. 57, pp. 41-51, 2005.
[22]C. H. Chen, Y. Kang and C. C. Huang, “The influences of orifice restriction and journal eccentricity on the stability of the rigid rotor-hybrid bearing system,” Tribology International, Vol. 37, pp. 227-234, 2004.
[23]C. H. Chen, Y. Kang, Y. N. Huang, C. H. Chu and J. T. Teng, “The restrictive effects of capillary compensation on the stability of the Jeffcott rotor-hybrid bearing system,” Tribology International, Vol. 35, pp. 849-855, 2002.
[24]C. H. Chen, Y. Kang, Y. N. Huang, C. H. Chu and J. T. Teng, “The restrictive effects of orifice compensation on the stability of the Jeffcott rotor-hybrid bearing system,” Industrial Lubrication and Tribology, Vol. 54, pp. 255-261, 2002.
[25]M. E. Mohsin, “The use of controlled restrictors for compensating hydrostatic bearing,” Proceedings of Third International Conference on Machine Tool Design Research, pp. 129-424, 1963.
[26]J. G. C. Degast, “A new type of controlled restrictors for compensating hydrostatic bearings,” Proceedings of Seventh International Conference on Machine Tool Design Research, pp. 8-273, 1966.
[27]S. A. Moris, “Passively and actively controlled externally pressurized oil-film bearing,” ASME Journal of Lubrication Technology, Vol. 94, pp. 56-63, 1972.
[28]G. kh. Ingert and B. G. Lur’e, “Dynamic stiffness of hydrostatic slides,” Machines and Tooling, Vol. 44, pp. 28-32, 1973.
[29]C. Cusano, “Characteristics of externally pressurized journal bearings with membrane type variable flow restrictor as compensating element,” IMechE, Vol. 188, pp. 52-74, 1974.
[30]Y. A. Sukholutskii, “Closed-loop hydrostatic slideways with regulators,” Stanknii Instrument, Vol. 46, pp. 15-18, 1975.
[31]孟心齋，「毛細管節流開式液體靜壓導軌油膜厚度─載荷特性的分析與改善特性的措施」，洛陽農機學院學報，第1期，第87-99頁，1981。
[32]G. K. Lewis, “The stiffness and static of compensated hydrostatic cylindrical-pad bearing,” Proceedings of the Institution of Mechanical Engineers, Vol. 198, pp. 285-292, 1984.
[33]C. Wang and C. Cusano, “Dynamic characteristcs of externally pressurized, double pad, circular thrust bearings with membrane restrictors,” ASME Journal of Tribology, Vol. 133, pp. 158-165, 1991.
[34]孟昭焱、孟心齋和陳樹賢，「開式液體靜壓導軌靜態性能與最佳參數」，洛陽工學院學報，第21卷，第43-47頁，2000。
[35]孟昭焱和孟心齋，「節流性能優異的新型液體靜壓支承節流器」，中國工程科學，第7卷，第3期，第49-52頁，2005。
[36]Y. Kang, P. C. Shen, Y. P. Chang, H. H. Lee and C. P. Chiang, “Modified predictions of restriction coefficient and flow resistance for membrane-tape restrictors in hydrostatic bearing by using regression,” Tribology International, Vol. 40, pp. 1369-1380, 2007.
[37]Y. Kang, P. C. Shen, Y. P. Chang and H. H. Lee, “Modified determination of fluid resistance for membrane-type restrictor,” Industrial Lubrication and Tribology, Vol. 59, pp. 123-131, 2007.
[38]朱有洪、劉建亭、楊建璽和白鍇，「液體靜壓軸承薄膜節流新結構的設計分析」，軸承，第3期第27-30頁，2008。
[39]D. E. Bently, A. Petchenev, T. Eldridge, “The death of whirl－What the SFCB can do for the stability of rotating machinery,” ORBIT, Vol. 21, pp. 10-13(2000).
[40]J. Hesselbach and C. Abel-Keihack, “Active hydrostatic bearing with magnetorheological fluid,” Proceedings 8th International Conference on New Actuators, pp. 343–346, 2002.
[41]J. Hesselbach and C. Abel-Keihack, “Active hydrostatic bearing with magnetorheological fluid,” Journal Applied Physics, Vol. 93, pp. 8441–8443, 2003.
[42]W. B. Rowe, Hydrostatic and Hybrid Bearing Design, London: Butterworths, 1983.
[43]B. F. Spencer, Jr, S. J. Dyke, M. K. Sain and J. D. Carlson, “Phenomenological model of a magnetorheological damper,” Journal of Engineering Mechanics, Vol. 123, pp. 230–238, 1997.
[44]W. H. Herschel and R. Bulkley, “Konsistenzmessungen von Gummi- Benzollösungen,” Kolloid Zeitschrift, Vol. 39, pp. 291–300. 1926.
[45]J. M. Guldbakke and J. Hesselbach, “Development of bearings and a damper based on magnetically controllable fluids,” Journal Physics: Condensed Matter, Vol. 18, pp. S2959–S2972, 2006.
[46]J. P. McTague, “Magnetoviscosity of magnetic colloids,” Journal of Chemistry Physics, Vol. 51, pp. 133–136, 1969.
[47]J. L. Neuringer and R. E. Rosensweig, “Ferrohydrodynamics,” Physics of Fluids, Vol. 7, pp. 1927–1937, 1964.
[48]M. I. Shliomis, “Effective viscosity of magnetic suspensions,” Soviet Physics JETP, Vol. 34, pp. 1291–1294, 1972.
[49]M. A. Martsenyuk, Yu. L. Raikher and M. I. Shliomis, “On the kinetics of magnetization of suspensions of ferromagnetic particles,” Soviet Physics JETP, Vol. 38, pp. 413–416, 1974.
[50]M. A. Leontovich, Introduction to Thermodynamics, Statistical Physics, Moskva: Nauka, 1983.
[51]A. O. Tsebers, “Numerical experiments on the simulation of the rotational Brownian motion of a ferromagnetic particle in a field,” Magnetohydrodynamics, Vol. 20, pp. 343–348, 1984.
[52]A. O. Tsebers, “Magnetization relaxation equations for a ferromagnetic colloid under highly nonequilibrium conditions,” Magnetohydrodynamics, Vol. 21, pp. 357–362, 1985.
[53]M. I. Shliomis, T. P. Lyubimova and D. V. Lyubimov, “Ferrohydrodynamics: An essay on the progress of ideas,” Chemical Engineering Communications, Vol. 67, pp. 275–290, 1988.
[54]M. I. Shliomis, “Comment on “Magnetoviscosity and relaxation in ferrofluids,” Physical Review E, Vol. 64, p. 063501, 2001a.
[55]M. I. Shliomis, “Ferrohydrodynamics: Testing a third magnetization equation,” Physical Review E, Vol. 64, p. 060501(R), 2001b.
[56]H. C. Weng and C. -K. Chen, “Comment on 'Measuring the transverse magnetization of rotating ferrofluids',” Physical Review E, Vol. 78, p. 068301, 2008.
[57]J. P. Ems, S. May, C. Wagner, A. V. Kityk, A. Leschhorn and M. Lücke, “Measuring the transverse magnetization of rotating ferrofluids,” Physical Review E, Vol. 73, p. 036302, 2006.
[58]H. C. Weng, C. -L. Chen and C.-K. Chen, “Non-Newtonian flow of dilute ferrofluids in a uniform magnetic field,” Physical Review E, Vol. 78, p. 056305, 2008.
[59]H. C. Weng, “Couple-stress effect on the effective viscosity of magnetic fluids,” Physics Procedia, Vol. 9, pp. 63-67, 2010.
[60]T. E. Tarapov, “Movement of a magnetizable fluid in the lubricating layer of a cylindrical bearing,” Magnitnaya Gidrodinamika, Vol. 4, pp.19-24, 1972.
[61]J. S. Walker and J. D. Buckmaster, “Ferrohydrodynamics thrust bearings,” International Journal of Engineering Science, Vol. 17, pp. 1171-1182, 1979.
[62]N. Tipei, “Theory of lubrication with ferrofluids application to short bearings,” ASME Journal of Lubrication, Vol. 104, pp.510-515, 1982.
[63]J. B. Shukla and D. J. Kumar, “A theory of ferrofluid lubrication, ” Journal of Magnetism and Magnetic Materials, Vol. 65, pp. 375-385, 1987.
[64]P. Sinha, P. Chandra Kanpur, D. Kumar, “Ferrofluid lubrication of cylindrical rollers with cavitaions, “ Acta Mechanica, Vol. 98, pp. 27-38, 1993.
[65]P. Ram and P. D. S. Verma, “Ferro fluid lubrication in porous inclined slider bearing,” Indian Journal of Pure Applied Mathematics, Vol. 30, pp. 1283-1281, 1990.
[66]J. T. Jenkins, “A theory of magnetic fluid,” Archive for Rational Mechanics and Analysis, Vol. 46, pp. 42-60, 1972.
[67]G. A. Maugin, “The principle of virtual power: application to coupled fields,” Acta Mechanics, Vol. 35, pp. 1-80, 1980.
[68]M. V. Bhat and G. M. Dehri, “Squeeze film behaviour in porous annular discs lubricated with magnetic fluid,” Wear, Vol. 151, pp.123-128, 1991.
[69]R. C. Shah and M.V. Bhat, “Squeeze film based on magnetic fluid in curved rotating circular plates” Journal of Magnetism and Magnetic Materials, Vol. 208, pp.115-119, 2000.
[70]R. C. Shah and M. V. Bhat, “Ferrofluid squeeze film in a long bearing,” Tribology International, vol. 37, pp. 441-446, 2004.
[71]V. K. Stokes, “Couple stress in fluids,” Physics of Fluids, Vol. 9, pp. 1709-1715, 1966.
[72]G. Ramanaiah, P. Sarkar, “Slider bearings lubricated by fluids with couple stress,” Wear, Vol. 52, pp. 27-36, 1979.
[73]G. Ramanaiah, “Optimal load capacity of a slider bearing lubricated by a fluid 92 with couple stress,” Wear, Vol. 49, pp. 61-66, 1978.
[74]P. Sinha and C. Singh, “Couple stresses in the lubrication of rolling contact bearings considering cavitation,” Wear, Vol. 67, pp. 85-98, 1981.
[75]N. M. Bujurke and N. B. Naduvinamani, “The lubrication of lightly loaded cylinders in combined rolling, sliding and normal motion with couple stress fluid,” International Journal of Mechanics and Science, Vol. 32, pp. 969-979, 1990.
[76]N. Das, “Elastohydrodynamic lubrication theory of line contacts: couple stress fluid model,” Tribology Transactions, Vol. 40, pp. 353-359, 1997.
[77]N. B. Naduvinamani, P. S. Hiremath and G. Gurubasavaraj, “Squeeze film lubrication of a short porous journal bearing with couple stress fluids,” Tribology International, Vol. 34, pp. 739-747, 2001.
[78]N. C. Das and R. C. Bhattacharjee, “Porous slider bearing lubricated with couple stress MHD fluids,” Transactions of CSME, Vol. 4, pp.317-331, 1994.
[79]N. C. Das, “A study of optimum load-bearing capacity for slider bearing lubricated with couple stress fluids in magnetic field,” Tribology International, Vol. 31, pp.393-400, 1998.